Introduction to Cryptography: Understanding the Science of Cryptology

INTRODUCTION TO CRYPTOGRAPHY Introductionto Cryptography 1/1 4/4/2025 NSEC

DISCLAIMERS 1 All the pictures used in this presentation are taken from freely available websites. 2 If there is a reference on a slide all of the information on that slide is attributable to that source whether quotation marks are used or not. 3 Any mention of commercial products or reference to commercial organizations is for information only; it does not imply recommendation or endorsement nor does it imply that the products mentioned are necessarily the best available for the purpose. January 3, 2024 2/1 4/4/2025 NSEC

Outline Introductionto Cryptography 4/4/2025 NSEC January 3, 2024 3/1

Introduction Outline January 3, 2024 4/1 4/4/2025 NSEC

Introduction What is Cryptography? Cryptology ation Technology, Introductionto NSEC January 3, 2024 5/1 4/4/2025

Introduction What is Cryptography? Cryptology Cryptology Cryptology Cryptography Cryptanalysis ation Technology, Lucknowddey@iiitl.ac.in) 4/4/2025 Introductionto Cryptography NSEC January 3, 2024 5/1

Introduction What is Cryptography? Cryptology Cryptology Cryptography: is a science which deals with how to achieve PAIN Cryptology Cryptology Cryptography Cryptanalysis ation Technology, Lucknowddey@iiitl.ac.in) 4/4/2025 Introductionto Cryptography NSEC January 3, 2024 5/1

Introduction What is Cryptography? Cryptology Cryptology Cryptography: is a science which deals with how to achieve PAIN Privacy & Confidentiality Authentication, Integrity & Non-repudiation. Cryptology Cryptology Cryptography Cryptanalysis Introductionto Cryptography NSEC 5/1 ) 4/4/2025

Introduction What is Cryptography? Cryptology Cryptology Cryptography: is a science which deals with how to achieve PAIN Privacy & Confidentiality Authentication, Integrity & Non-repudiation. Cryptanalysis: is a science which deals with how to defeat of achieving PAIN Cryptology Cryptology Cryptography Cryptanalysis ation Technology, Lucknowddey@iiitl.ac.in) Introductionto Cryptography 4/4/2025 NSEC January 3, 2024 5/1

Introduction What is Cryptography? Cryptology Cryptology Cryptography: is a science which deals with how to achieve PAIN Privacy & Confidentiality Authentication, Integrity & Non-repudiation. Cryptanalysis: is a science which deals with how to defeat of achieving PAIN Cryptology Cryptology Cryptography Cryptanalysis Cryptography is about communication in the presence of an adversary. Rivest ation Technology, Lucknowddey@iiitl.ac.in) 4/4/2025 Introductionto Cryptography NSEC January 3, 2024 5/1

Introduction What is Cryptography? Cryptology Cryptology Cryptography: is a science which deals with how to achieve PAIN Privacy & Confidentiality Authentication, Integrity & Non-repudiation. Cryptanalysis: is a science which deals with how to defeat of achieving PAIN Cryptology Cryptology Cryptography Cryptanalysis Cryptography is about communication in the presence of an adversary. Rivest The Concise Oxford English Dictionary defines cryptography as "the art of writing or solving codes." ation Technology, Lucknowddey@iiitl.ac.in) 4/4/2025 Introductionto Cryptography NSEC January 3, 2024 5/1

Introduction What is Cryptography? Cryptography Cryptography supports multiple goals ation Technology, Lucknowddey@iiitl.ac.in) 4/4/2025 Introductionto Cryptography NSEC January 3, 2024 6/1

Introduction Cryptography for Secure Communication ation Technology, Lucknowddey@iiitl.ac.in) 4/4/2025 Introductionto Cryptography NSEC January 3, 2024 7/1

Introduction Cryptography for Secure Communication Text/Speech/ Encoding Fax/Image 4/4/2025 NSEC

Introduction CRYPTOGRAPHY FOR SECURE COMMUNICATION Text/Speech/ Encoding Compression Fax/Image Encryption 4/4/2025 NSEC

Introduction CRYPTOGRAPHY FOR SECURE COMMUNICATION Text/Speech/ Encoding Compression Fax/Image Key Encryption 4/4/2025 NSEC

Introduction CRYPTOGRAPHY FOR SECURE COMMUNICATION Text/Speech/ Encoding Compression Fax/Image Key Encryption Steganography (Optional) ation Technology, Lucknowddey@iiitl.ac.in) Introductionto Cryptography NSEC January 3, 2024 7/1 4/4/2025

Introduction CRYPTOGRAPHY FOR SECURE COMMUNICATION Text/Speech/ Encoding Compression Fax/Image Key Encryption Wiredor Wireless Modulation ErrorControl ation Technology, Lucknowddey@iiitl.ac.in) Introductionto Cryptography NSEC January 3, 2024 8/1 4/4/2025

Introduction Cryptographyvs. Security Cryptography vs. Security Information securityincludes the study of subjects like: Computersecurity Network security Software security ation Technology, Lucknowddey@iiitl.ac.in) 4/4/2025 Introductionto Cryptography NSEC January 3, 2024 9/1

Introduction Cryptographyvs. Security Cryptography vs. Security Information securityincludes the study of subjects like: Computersecurity Network security Software security Cryptographyprovides some mathematical tools that can assist with the provision of information security services. It is asmallbut essential partof a complete solution. ation Technology, Lucknowddey@iiitl.ac.in) 4/4/2025 Introductionto Cryptography NSEC January 3, 2024 9/1

Introduction Cryptographyvs. Security Cryptography vs. Security Information securityincludes the study of subjects like: Computersecurity Network security Software security Cryptographyprovides some mathematical tools that can assist with the provision of information security services. It is asmallbut essential partof a complete solution. Securityis a chain Weak links become targets One flaw is all it takes January 3, 2024 9/1 4/4/2025 NSEC

Introduction Cryptographyvs. Security Cryptography vs. Security Information securityincludes the study of subjects like: Computersecurity Network security Software security Cryptographyprovides some mathematical tools that can assist with the provision of information security services. It is asmallbut essential partof a complete solution. Securityis a chain Weak links become targets One flaw is all it takes (Door locks Home security) Cryptography is usuallynot the weakest link(however, when the crypto fails the damage can be catastrophic) ation Technology, Lucknowddey@iiitl.ac.in) 4/4/2025 Introductionto Cryptography NSEC January 3, 2024 9/1

Introduction Cryptographyvs. Security 10 Cyber-security Domains Information Security & Risk Management AccessControl Business Continuity & DisasterRecovery Physical EnvironmentalSecurity Legal, Regulations, Compliance Investigations Operations Security Security Architecture & Design Telecommunications & Network Security Application Security & Cryptography & Table: International Information Systems Security Consortium s 10 Domains G. J. Touhill & C. J. Touhill, Cyber-security for Executives: A Practical Guide, Wiley, 2014. ation Technology, Lucknowddey@iiitl.ac.in) 4/4/2025 Introductionto Cryptography NSEC

Introduction Cryptographyvs. Security Components of Cryptosystems ation Technology, Lucknowddey@iiitl.ac.in) 4/4/2025 Introductionto Cryptography NSEC 11/1

Introduction Cryptographyvs. Security Components of Cryptosystems . Plaintext-space: P a set of plaintexts over an alphabet Ciphertext-space: C a set of ciphertexts over alphabet Key-space: K a set of keys ation Technology, Lucknowddey@iiitl.ac.in) 4/4/2025 Introductionto Cryptography NSEC 11/1

Introduction Cryptographyvs. Security Components of Cryptosystems . Plaintext-space: P a set of plaintexts over an alphabet Ciphertext-space: C a set of ciphertexts over alphabet Key-space: K a set of keys Each key k determines an encryption algorithm ek and an decryption algorithm dk such that, for any plaintext w, ek(w) is the corresponding ciphertext and w = dk(ek(w)). ation Technology, Lucknowddey@iiitl.ac.in) 4/4/2025 Introductionto Cryptography NSEC 11/1

Introduction Cryptographyvs. Security Cryptosystems Definition Acryptosystemis a five-tuple (P,C, K, E,D), where P is a finite set of possibleplaintexts, C is a finite set of possibleciphertexts, K, the keyspace, is a finite set ofpossible keys, For each K K, there is an encryption rule eK E and a corresponding decryption rule dK D. Each (i) (ii) (iii) (iv) eK : P C and dK : C P are functions s/t dK(eK(x)) = x for every plaintext element x P. ation Technology, Lucknowddey@iiitl.ac.in) 4/4/2025 Introductionto Cryptography NSEC

Introduction Cryptographyvs. Security Requirements for Good Cryptosystems ation Technology, Lucknowddey@iiitl.ac.in) 4/4/2025 Introductionto Cryptography NSEC 13/1

Introduction Cryptographyvs. Security Requirements for Good Cryptosystems Given ek and a plaintext w, it should be easy to compute c = ek(w). Given dk and a ciphertext c, it should be easy to compute w = dk(c). ation Technology, Lucknowddey@iiitl.ac.in) 4/4/2025 Introductionto Cryptography NSEC 13/1

Introduction Cryptographyvs. Security Requirements for Good Cryptosystems Given ek and a plaintext w, it should be easy to compute c = ek(w). Given dk and a ciphertext c, it should be easy to compute w = dk(c). A ciphertext ek(w) should not bemuch longer thanthe plaintext w. ation Technology, Lucknowddey@iiitl.ac.in) 4/4/2025 Introductionto Cryptography NSEC 13/1

Introduction Cryptographyvs. Security Requirements for Good Cryptosystems Given ek and a plaintext w, it should be easy to compute c = ek(w). Given dk and a ciphertext c, it should be easy to compute w = dk(c). A ciphertext ek(w) should not bemuch longer thanthe plaintext w. It should beinfeasibleto determine w from ek(w) without knowing dk. ation Technology, Lucknowddey@iiitl.ac.in) 4/4/2025 Introductionto Cryptography NSEC 13/1

Introduction Cryptographyvs. Security Requirements for Good Cryptosystems Given ek and a plaintext w, it should be easy to compute c = ek(w). Given dk and a ciphertext c, it should be easy to compute w = dk(c). A ciphertext ek(w) should not bemuch longer thanthe plaintext w. It should beinfeasibleto determine w from ek(w) without knowing dk. The so calledavalanche effectshould hold. ation Technology, Lucknowddey@iiitl.ac.in) 4/4/2025 Introductionto Cryptography NSEC 13/1

Introduction Cryptographyvs. Security Requirements for Good Cryptosystems Given ek and a plaintext w, it should be easy to compute c = ek(w). Given dk and a ciphertext c, it should be easy to compute w = dk(c). A ciphertext ek(w) should not bemuch longer thanthe plaintext w. It should beinfeasibleto determine w from ek(w) without knowing dk. The so calledavalanche effectshould hold. The cryptosystem shouldnot be closed under composition, i.e. not for every two keys k1,k2 a key k s/t ek(w) = ek1(ek2(w)). The set of keys should bevery large. ation Technology, Lucknowddey@iiitl.ac.in) 4/4/2025 Introductionto Cryptography NSEC 13/1

Introduction Cryptographyvs. Security A Generic View of Secret Key Crypto key key encrypt decrypt plaintext plaintext ciphertext ation Technology, Lucknowddey@iiitl.ac.in) 4/4/2025 Introductionto Cryptography NSEC 14/1

Introduction Cryptographyvs. Security A Generic View of Secret Key Crypto key key encrypt decrypt plaintext plaintext ciphertext Sender and receiver use the same key Sender and receiver are equivalent The oldest type of cryptography Gives the best performance Provides highest security standards ation Technology, Lucknowddey@iiitl.ac.in) 4/4/2025 Introductionto Cryptography NSEC 14/1

Introduction Cryptographyvs. Security A Generic View of Secret Key Crypto key key encrypt decrypt plaintext plaintext ciphertext Sender and receiver use the same key Sender and receiver are equivalent The oldest type of cryptography Gives the best performance Provides highest security standards Only disadvantage: ation Technology, Lucknowddey@iiitl.ac.in) 4/4/2025 Introductionto Cryptography NSEC 14/1

Introduction Cryptographyvs. Security A Generic View of Secret Key Crypto key key encrypt decrypt plaintext plaintext ciphertext Sender and receiver use the same key Sender and receiver are equivalent The oldest type of cryptography Gives the best performance Provides highest security standards Only disadvantage: difficult key management ation Technology, Lucknowddey@iiitl.ac.in) 4/4/2025 Introductionto Cryptography NSEC

Introduction Cryptographyvs. Security Secret Key Crypto Classification Secret Key Cryptography Block Stream MAC ation Technology, Lucknowddey@iiitl.ac.in) 4/4/2025 Introductionto Cryptography NSEC

Introduction Cryptographyvs. Security A Generic View of Public Key Crypto public key privatekey encrypt decrypt plaintext plaintext ciphertext ation Technology, Lucknowddey@iiitl.ac.in) 4/4/2025 Introductionto Cryptography NSEC 16/1

Introduction Cryptographyvs. Security A Generic View of Public Key Crypto public key privatekey encrypt decrypt plaintext plaintext ciphertext Advantages over symmetric-key Better key distribution and management 1 No danger that public key compromised New protocols 2 Digital Signature Long-termencryption 3 ation Technology, Lucknowddey@iiitl.ac.in) 4/4/2025 Introductionto Cryptography NSEC 16/1

Introduction Cryptographyvs. Security A Generic View of Public Key Crypto public key privatekey encrypt decrypt plaintext plaintext ciphertext Advantages over symmetric-key Better key distribution and management 1 No danger that public key compromised New protocols 2 Digital Signature Long-termencryption 3 Onlydisadvantage: ation Technology, Lucknowddey@iiitl.ac.in) 4/4/2025 Introductionto Cryptography NSEC 1641/ 1

Introduction Cryptographyvs. Security A Generic View of Public Key Crypto public key privatekey encrypt decrypt plaintext plaintext ciphertext Advantages over symmetric-key Better key distribution and management 1 No danger that public key compromised New protocols 2 Digital Signature Long-termencryption 3 Only disadvantage: much more slower than symmetric key crypto ation Technology, Lucknowddey@iiitl.ac.in) 4/4/2025 Introductionto Cryptography NSEC

Introduction Cryptographyvs. Security Public Key Crypto Classification Public Key Cryptography Conventional Post-Quantum Isogeny IF-based DLP-based Lattice Code MPKC Hash 4/4/2025 NSEC

Introduction Cryptographyvs. Security Hybrid Cryptography Drawbackof PKC much slower than secret-key Crypto Drawback of secret-key Crypto key management ation Technology, Lucknowddey@iiitl.ac.in) 4/4/2025 Introductionto Cryptography NSEC 18/1

Introduction Cryptographyvs. Security Hybrid Cryptography Drawbackof PKC much slower than secret-key Crypto Drawback of secret-key Crypto key management Hybrid cryptography: to take the benefits of both Apply PKC to encrypt the the secret key k Use secret key k to encrypt the message M ation Technology, Lucknowddey@iiitl.ac.in) 4/4/2025 Introductionto Cryptography NSEC 18/1

Introduction Cryptographyvs. Security Principle The philosophy of modern cryptanalysis is embodied in the following principle formulated in 1883 Basic assumptions: The system is completely known to the attacker Only the key is secret That is, crypto algorithms are not secret ation Technology, Lucknowddey@iiitl.ac.in) 4/4/2025 Introductionto Cryptography NSEC 19/1

Introduction Cryptographyvs. Security Principle The philosophy of modern cryptanalysis is embodied in the following principle formulated in 1883 Basic assumptions: The system is completely known to the attacker Only the key is secret That is, crypto algorithms are not secret This is known as Kerckhoffs Principle ation Technology, Lucknowddey@iiitl.ac.in) 4/4/2025 Introductionto Cryptography NSEC 19/1

Introduction Cryptographyvs. Security Principle The philosophy of modern cryptanalysis is embodied in the following principle formulated in 1883 Basic assumptions: The system is completely known to the attacker Only the key is secret That is, crypto algorithms are not secret This is known as Kerckhoffs Principle Why do we make this assumption? ation Technology, Lucknowddey@iiitl.ac.in) 4/4/2025 Introductionto Cryptography NSEC 19/1

Introduction Cryptographyvs. Security Principle The philosophy of modern cryptanalysis is embodied in the following principle formulated in 1883 Basic assumptions: The system is completely known to the attacker Only the key is secret That is, crypto algorithms are not secret This is known as Kerckhoffs Principle Why do we make this assumption? Easier to maintain secrecy of a short keyrather than an algorithm ation Technology, Lucknowddey@iiitl.ac.in) 4/4/2025 Introductionto Cryptography NSEC 19/1

Introduction Cryptographyvs. Security Principle The philosophy of modern cryptanalysis is embodied in the following principle formulated in 1883 Basic assumptions: The system is completely known to the attacker Only the key is secret That is, crypto algorithms are not secret This is known as Kerckhoffs Principle Why do we make this assumption? Easier to maintain secrecy of a short keyrather than an algorithm Algorithm parts may be leaked: insider or reverse engineering. ation Technology, Lucknowddey@iiitl.ac.in) 4/4/2025 Introductionto Cryptography NSEC 19/1